06-18-2026, 06:02 PM
![[Image: 960px-Illustration_of_great-circle_distance.svg.png]](https://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Illustration_of_great-circle_distance.svg/960px-Illustration_of_great-circle_distance.svg.png)
Haversine formula [wikipedia]
Summary
The Haversine formula is a fundamental equation in spherical trigonometry used to calculate the shortest distance (the great-circle distance) between two points on a sphere from their latitudes and longitudes, making it especially important in navigation, GPS systems, mapping software, and geospatial applications. It is based on the haversine function, defined as $( \operatorname{hav}(\theta)=\sin^2(\theta/2) )$, and provides a numerically stable way to compute distances even when points are very close together.
Developed from the law of haversines, the formula became widely used by navigators in the 19th century, with the term “haversine” coined by James Inman in 1835. Before computers, tables of haversine values simplified calculations, while today the formula remains a standard tool for estimating distances on the Earth, which is often approximated as a sphere.
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